## Thursday, 4 August 2016

### III. Rising rate of productivity of the additional capital.

With rising marginal productivity of capital, the additional output required to exclude land type A, is achieved more quickly than where marginal productivity is constant or falling. If the marginal productivity rises evenly, across all soil types, the difference will be made up more quickly where the extra investment occurs on more fertile soil. If it rises more rapidly on the better soil, that will be enhanced, and vice versa where marginal productivity rises more quickly on the less fertile soil.

“In so far as this varying effect balances out the differences, or accentuates them, the differential rent of the better soils, and thereby the total rental too, will fall or rise, as was already the case in differential rent I. In other respects, everything depends upon the magnitude of the land area and capital excluded together with A, and upon the relative magnitude of advanced capital required with a rising productivity in order to produce the additional output to meet the demand.” (p 703)

Where the price of production remained the same, it didn't matter whether the marginal productivity of capital was rising, falling or constant, because land type A continued to regulate the price of production.

Where the price of production was falling, this could only be because land type A no longer regulated the price of production. If the marginal productivity of capital was constant, that could only occur where production on land type B - D rose sufficiently to make A's output redundant. That is all the more the case where the marginal productivity of capital is falling, because any additional investment in land A would cause the price of production to rise.

However, where the marginal productivity of capital is rising, the price of production may fall, even if this additional capital is invested in land type A.

Table 10

 Type of Soil Ha. Capital £ Profit £ Price of Production £ Output Kilos Selling price £ Proceeds £ Rent Rate of Surplus Profit Kilos £ A 1 2.5 + 2.5 = 5 1.00 6.00 1 + 1.2 =2.2 2 .73 6.00 0 0 0% B 1 2.5 + 2.5 = 5 1.00 6.00 2 + 2.4 = 4.4 2.73 12.00 2.2 6.00 120% C 1 2.5 + 2.5 = 5 1.00 6.00 3 + 3.6 = 6.6 2.73 18.00 4.4 12.00 240% D 1 2.5 + 2.5 = 5 1.00 6.00 4 + 4.8 = 8.8 2.73 24.00 6.6 18.00 360% 4 20 4 24.00 22 60.00 13.2 36.00 240%
This table can be compared with Table 1.

Table 1.

 Type of soil Ha. Capital £ Profit £ Price of Prod. £ Output Kilos Selling Price £ Proceeds £ Rent Rate of Surplus Profit Kilos £ A 1 2.50 0.50 3.00 1 3.00 3.00 0 0 0 B 1 2.50 0.50 3.00 2 3.00 6.00 1 3.00 120% C 1 2.50 0.50 3.00 3 3.00 9.00 2 6.00 240% D 1 2.50 0.50 3.00 4 3.00 12.00 3 9.00 360% Total 4 10.00 2.00 12.00 10 30.00 6 18.00 180%
And with Table 2.

Table 2.

 Type of soil Ha. Capital £ Profit £ Price of Prod. Output Kilos Selling Price £ Proceeds £ Rent Surplus Profit Kilos £ A 1 2.50 + 2.50 = 5 1.00 6.00 2 3.00 6.00 0 0 0 B 1 2.50 + 2.50 = 5 1.00 6.00 4 3.00 2.00 2 6.00 120% C 1 2.50 + 2.50 = 5 1.00 6.00 6 3.00 18.00 4 12.00 240% D 1 2.50 + 2.50 = 5 1.00 6.00 8 3.00 24.00 6 18.00 360% Total 4 20.00 4.00 24.00 20 60.00 12 36.00 180%
The price of production for the output of A here remains £6 - £5 capital invested, plus 20% average profit. However, the price of production per kilo has fallen from £3 to £2.73, because A now produces 2.2 kilos, rather than the 2 kilos that would previously have resulted from an investment of £5 of capital with constant marginal productivity.

“Since the rate of productivity increases with the additional investment of capital, this presupposes an improvement. The latter may consist of a general increase in capital invested per acre (more fertiliser, more mechanised labour, etc.), or it may be that only through this additional capital it is at all possible to bring about a qualitatively different more productive investment of the capital. In both cases, the investment of £5 of capital per acre yields an output of 2 1/5 qrs, whereas the investment of one-half of this capital, i.e., £2 1/2, yields only 1 qr of produce. The produce from soil A could, regardless of transient market conditions, only continue to be sold at a higher price of production instead of at the new average price, as long as a considerable area of type A soil continued to be cultivated with a capital of only £2½ per acre. But as soon as the new relation of £5 of capital per acre, and thereby the improved management, becomes universal, the regulating price of production would have to fall to £2 8/11.” (p 704-5)

The lower productivity of type A land would only persist where it was farmed using inadequate levels of capital, i.e. £2.50 per hectare rather than £5 per hectare.

“This shows, first of all, that insufficient capital in the hands of a large number of tenant farmers (it must be a large number, for a small number would simply be compelled to sell below their price of production) produces the same effect as a differentiation of the soils themselves in a descending line. The inferior cultivation of inferior soil increases the rent from superior soils; it may even lead to rent being yielded from better cultivated soil of equally poor quality, which would otherwise not be yielded.” (p 705)

Marx's comment that it must be a large number of tenant farmers seems to contradict his assumption that the average rate of profit is paid on the worst land, whose output is required to meet the level of demand. Moreover, its not clear that a large number of such small farmers are in a stronger position here to demand such a level of prices than a small number. For any given level of output from land type A, a large number of producers implies smaller sized farms, and greater competition between them, and a weaker position for each individual farm.

“It shows, secondly, that differential rent, in so far as it arises from successive investments of capital in the same total area, resolves itself in reality into an average, in which the effects of the various investments of capital are no longer recognisable and distinguishable, and therefore do not result in rent being yielded from the worst soil, but rather: 1) make the average price of the total yield for, say, an acre of A, the new regulating price and 2) appear as alteration in the total quantity of capital per acre required under the new conditions for the adequate cultivation of the soil; and in which the individual successive investments of capital, as well as their respective effects, will appear indistinguishably blended together. It is exactly the same with the individual differential rents from the superior soils. In each case, they are determined by the difference between the average output from the soil in question and the output from the worst soil at the increased capital investment — which has now become normal.” (p 705)

Even under Differential Rent I, land only produces output on the basis of the investment of capital, and as with each industry, at any particular time, there is a minimum level of capital investment required for production at an efficient level. Over a period, this minimum level of investment will rise. If, however, the majority of land type A does not receive such additional investment, it will continue to determine the price of production, provided output does not rise so as to push it out of production. Those pieces of land type A that do receive the additional investment will produce surplus profits, and produce rent, whilst land types B – D, on the basis of the higher level of investment, will produce more surplus profit and rent.

“But as soon as the new method of cultivation has become general enough to be the normal one, the price of production falls; the rent from the superior plots declines again, and that portion of soil A that does not possess the working capital, which has now become the average, must sell its produce below its individual price of production, i.e., below the average profit.” (p 706)

This also applies where the marginal productivity of capital is falling, in so far as its investment on the better lands increases output and pushes out land type A.

“The quantity of capital which is now required, on an average, to be invested in the better soil B, the new regulator, now becomes normal: and when one speaks of the varying fertility of plots of land, it is assumed that this new normal quantity of capital per acre is employed.” (p 706)

This minimum required level of capital was also important in the negotiation of leases.

“... it is evident that this average investment of capital, say, in England, of £8 per acre prior to 1848, and £12 subsequent to that year, will constitute the standard in concluding leases. For the farmer expending more than this, the surplus-profit is not transformed into rent for the duration of the contract. Whether this takes place after expiration of the contract or not will depend upon the competition among the farmers who are in a position to make the same extra capital advance. We are not referring here to such permanent soil improvements that continue to provide the increased output with the same or even with a decreasing outlay of capital. Such improvements, although products of capital, have the same effect as natural differences in the quality of the land.” (p 706-7)

Differential Rent I continues to exist, independently of any changes in the normal or minimum level of capital investment, because it is based on the relative fertility of the soil, assuming the same capital invested. But, Differential Rent II is affected by changes in the minimum level of investment because any land that does not obtain this investment thereby not only does not pay rent, but must sell below the price of production, some elements of land type A may become rentable, whilst the rise in the minimum level may may increase output, so as to push out land type A. Marx does not consider the other option here that supply rises, but rather than being pushed out of production, type A producers simply sell at prices below their price of production, which could also have the effect of reducing market prices below the price of production of land type B.

Table 10 shows that grain rent has doubled compared with Table 1 and risen by 1.2 kilos compared to Table 2. Money rent doubled compared with Table 1, but was unchanged compared with Table 2. If more capital were invested in the better soils, the rent would have been much higher. Alternatively, if the additional capital invested in A had less impact on raising its output, the price of production would have been higher, so that surplus profit on the other land types would be higher.

Varying levels of marginal productivity from capital invested in the different land types would cause a change in the differential rent of each.

So, the rent per hectare may more than double, even if the additional capital increases by less than double, and this same rise in productivity causes the price of production to fall.

“But it may also fall if the price of production should fall much lower as a result of a more rapid increase in productiveness of soil A.” (p 707)

If the marginal productivity of capital, invested in A rises, compared to the marginal productivity of capital invested in B and C, the money rent from D would remain unchanged, but would fall from B and C, as indicated in Table 11.

Table 11

 Type of Soil Ha. Capital £ Profit £ Output Per Ha. Kilos Selling Price Proceeds £ Grain-Rent Kilos Money-Rent £ A 1 2.50+2.50 = 5.00 1 1+3=4 1.50 6.00 0 0 B 1 2.50 + 2.50 = 5.00 1 2 + 2.5 = 4.5 1.50 6.75 0.5 0.75 C 1 2.50 + 2.50 = 5.00 1 3 + 5 = 8 1.50 12.00 4 6.00 D 1 2.50 + 2.50 = 5.00 1 4 + 12 = 16 1.50 24.00 12 18.00 Total 4 20.00 32.5 48.75 16.5 24.75
The money rent would rise if more capital was invested in the better soils than A, so long as the marginal productivity was at least as good as obtained on A. Alternatively, if the same additional amounts were invested, but with a higher marginal productivity obtained from the investment in the better soils than A, the money rent would also rise.

The money rent falls where the additional investment of capital eradicates the differences in soil fertility that underpin Differential Rent I. It would also fall if it affect A more than B and C.

“The smaller the increase in productivity of the superior soils, the more it falls. It depends upon the extent of inequality produced, whether the grain-rent shall rise, fall or remain stationary.” (p 708)

There is a relative rise in rent, wherever the increased output is due to the investment of additional capital, rather than simply greater soil fertility with the same investment of capital.

“This is the absolute point of view, which shows that here, as in all former cases, the rent and increased rent per acre (as in the case of differential rent I on the entire cultivated area — the magnitude of the average rental) are the result of an increased investment of capital in land, no matter whether this capital functions with a constant rate of productivity at constant or decreasing prices or with a decreasing rate of productivity at constant or falling prices, or with an increasing rate of productivity at falling prices.” (p 708-9)

The basic reason for this is that Differential Rent I is based on the relative soil fertility, and if soil fertility rises, prices of production fall, but the relative differences remain.

“For our assumption: constant prices with a constant, falling, or rising rate of productivity of the additional capital, and falling prices with a constant, falling, or rising rate of productivity, resolves itself into: a constant rate of productivity of the additional capital at constant or falling prices, a falling rate of productivity at constant or falling prices, and a rising rate of productivity at constant and falling prices. Although the rent may remain stationary, or may fall, in all these cases, it would fall more if the additional investment of capital, other circumstances remaining the same, were not a prerequisite for the increased productiveness. The additional capital, then, is always the cause for the relatively high rent, although absolutely it may have decreased.” (p 709)